Publications mathématiques de l'IHÉS

, Volume 34, Issue 1, pp 53–104 | Cite as

Quasi-conformal mappings inn-space and the rigidity of hyperbolic space forms

  • G. D. Mostow


Conformal Mapping Quasiconformal Mapping Stereographic Projection Tubular Neighborhood Compact Riemann Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    L. V. Ahlfors, On quasi-conformal mappings,J. Analyse Math.,3 (1954), 1–58.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    A. Borel, Density properties for certain subgroups of semi-simple groups without compact components,Ann. of Math.,72 (1960), 179–188.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    J. A. Clarkson, Uniformly convex spaces,Trans. Amer. Math. Soc.,40 (1936), 396–414.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    E. Di Giorgi, Su una teoria generale della misura (r—1)-dimensionale in un spazio adr dimensioni,Ann. Mat. Pura Appl. Der., (4)36 (1954), 191–213.CrossRefzbMATHGoogle Scholar
  5. [5]
    ——, Sulla differenziabilita e l’analiticita della estremali degli integrali multipli regolari,Mem. Accad. Sci Torino Cl. Sci Fis. Mat. Nat.,3 (1957), 25–43.MathSciNetzbMATHGoogle Scholar
  6. [6]
    H. Federer, Curvature measures,Trans. Amer. Math. Soc.,93 (1959), 418–491.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    F. W. Gehring, Symmetrization of rings in space,Trans. Amer. Math. Soc.,101 (1961), 499–519.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    ——, Rings and quasi-conformal mappings in space,Trans. Amer. Math. Soc.,103 (1962), 353–393.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    H. Lebesgue, Sur le problème de Dirichlet,Rend. Circ. Palermo,24 (1907), 371–402.CrossRefzbMATHGoogle Scholar
  10. [10]
    C. Loewner, On the conformal capacity in space,J. Math. Mech.,8 (1959), 411–414.MathSciNetzbMATHGoogle Scholar
  11. [11]
    F. I. Mautner, Geodesic flows on symmetric Riemannian spaces,Annals of Math.,65 (1957), 416–431.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    A. Mori, On quasi-conformality and pseudo-analyticity,Trans. Amer. Math. Soc.,84 (1957), 56–77.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    J. Moser, A new proof of di Giorgi’s theorem concerning the regularity problem for elliptic differential equations,Comm. Pure Appl. Math.,13 (1960), 457–468.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    G. D. Mostow, Homogeneous spaces of finite invariant measure,Ann. of Math.,75 (1962), 17–37.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    ——, On the conjugacy of subgroups of semi-simple groups,Proc. of Symposia in Pure Math.,9 (1966), 413–419.MathSciNetCrossRefGoogle Scholar
  16. [16]
    R. Nevanlinna, On differentiable mappings,Analytic Functions, Princeton Univ. Press (1960), 3–9.Google Scholar
  17. [17]
    H. Rademacher, Partielle und totale Differenzierbarkeit von Funktionen mehrerer Variabeln,Math. Annalen,79 (1919), 340–359.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    S. Saks,Theory of the integral, Warsaw, 1937.Google Scholar
  19. [19]
    W. Stepanoff, Sur les conditions de l’existence de la differentielle totale,Rec. Math. Soc. Moscow,32 (1925), 511–526.zbMATHGoogle Scholar
  20. [20]
    O. Teichmuller, Untersuchungen über konforme und quasi-konforme Abbildungen,Deutsche Mathematik,3 (1938), 621–678.zbMATHGoogle Scholar

Copyright information

© Publications mathématiques de l’I.H.É.S 1968

Authors and Affiliations

  • G. D. Mostow
    • 1
  1. 1.Yale Univ. and I.H.E.S.USA

Personalised recommendations